We show that a scanning light beam can be focused below the diffraction limit without the control of moving near-field elements using the combination of two main components: a light-controlled saturable absorber, which creates seed evanescent components from the beam, and a layer of negative-refraction material, which amplifies the evanescent waves. Focusing to spots with a FWHM in the range of $0.2–0.3\lambda$ is predicted. For slightly off-resonant input beams, an intensity-dependent phase shift leads to smaller spots.

The wake of two oscillating cylinders in a tandem arrangement is a nonlinear system that displays Arnold tongues. We show by numerical simulations that their geometry depends on the phase difference $\theta$ between the two oscillating cylinders. At $\theta =0$ there may be holes inside these intraresonance regions unlike the solid Arnold tongues encountered in single-cylinder oscillations. This implies that, surprisingly, self-excitation of the system may be suppressed inside these holes, at conditions close to its natural frequency.

In this Letter, we study the scattering of light by a single subwavelength slit in a metal screen. In contrast with previous theoretical works, we provide a microscopic description of the scattering process by emphasizing the generation of surface plasmons at the slit apertures. The analysis is supported by a rigorous formalism based on a normal-mode-decomposition technique and by a semianalytical model that provides accurate formulas for the plasmonic generation strengths. The generation is shown to be fairly efficient for metals with a low conductivity, such as gold in the visible regime. Verification of the theory is also shown by comparison with recent experimental data [H. F. Schouten et al., Phys. Rev. Lett. 94, 053901 (2005)].

In channel flows a step on the route to turbulence is the formation of streaks, often due to algebraic growth of disturbances. While a variation of viscosity in the gradient direction often plays a large role in laminar-turbulent transition in shear flows, we show that it has, surprisingly, little effect on the algebraic growth. Nonuniform viscosity therefore may not always work as a flow-control strategy for maintaining the flow as laminar.

Nearly-steady-state locked intrinsic localized modes (ILMs) in the quasi-1D antiferromagnet $({\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{NH}}_3{)}_2{\mathrm{CuCl}}_4$ are detected via four-wave mixing emission or the uniform mode absorption. Exploiting the long-time stability of these locked ILMs, repeatable nonlinear switching is observed by varying the sample temperature, and localized modes with various amplitudes are created by modulation of the microwave driver power. This steady-state ILM locking technique could be used to produce energy localization in other atomic lattices.

Numerous nonlinear driven systems display spectacular responses to forcing, including chaos and complex phase-locking plateaus characterized by “devil’s staircase,” Arnold tongues, and Farey trees. In the universality class of Hamiltonian systems, a paradigm is the motion of a charged particle in two waves, which inspired a renormalization group method for its description. Here we report the observation of the underlying “devil’s staircase” by recording the beam velocity distribution function at the outlet of a traveling wave tube versus the amplitude of two externally induced waves.

Analysis of the frictional motion of a uniform circular disk of radius $R$ sliding and spinning on a horizontal table reported by Farkas et al. [Phys. Rev. Lett. 90, 248302 2003] shows that the disk always stops sliding and spinning at the same instant with a terminal speed ratio ${ϵ}_0=v/R\omega =0.653$. We show that different terminal behaviors can be found when one considers the motion of a two-tier disk with lower section thickness $H_1$ and radius $R_1$, and upper section thickness $H_2$ and radius $R_2$. The terminal motion may be analyzed in terms of the normalized radius of gyration $k$. It is found that while translation and rotation cease simultaneously, their terminal ratio ${ϵ}_0$ either vanishes when $k>\sqrt{2/3}$, is a nonzero constant when $1/2<k<\sqrt{2/3}$, or diverges when $k<1/2$. Experiments performed with plastic disks sliding on a nylon fabric stretched over a horizontal plate qualitatively corroborate the three different types of terminal motion.

We investigate the locality of interactions in hydrodynamic turbulence using data from a direct numerical simulation on a grid of ${1024}^3$ points; the flow is forced with the Taylor-Green vortex. An inertial range for the energy is obtained in which the flux is constant and the spectrum follows an approximate Kolmogorov law. Nonlinear triadic interactions are dominated by their nonlocal components, involving widely separated scales. The resulting nonlinear transfer itself is local at each scale but the step in the energy cascade is independent of that scale and directly related to the integral scale of the flow. Interactions with large scales represent 20% of the total energy flux. Possible explanations for the deviation from self-similar models, the link between these findings and intermittency, and their consequences for modeling of turbulent flows are briefly discussed.

We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schrödinger equation as a representative model. We formulate a thermodynamic description of the classical condensation process by using a wave turbulence theory with ultraviolet cutoff. In three dimensions the equilibrium state undergoes a phase transition for sufficiently low energy density, while no transition occurs in two dimensions, in complete analogy with standard Bose-Einstein condensation in quantum systems. On the basis of a modified wave turbulence theory, we show that the nonlinear interaction makes the transition to condensation subcritical. The theory is in quantitative agreement with the numerical integration of the nonlinear Schrödinger equation.

A new transient regime in the relaxation towards absolute equilibrium of the conservative and time-reversible 3D Euler equation with a high-wave-number spectral truncation is characterized. Large-scale dissipative effects, caused by the thermalized modes that spontaneously appear between a transition wave number and the maximum wave number, are calculated using fluctuation dissipation relations. The large-scale dynamics is found to be similar to that of high-Reynolds number Navier-Stokes equations and thus obeys (at least approximately) Kolmogorov scaling.

We demonstrate via numerical simulation that in the strongly nonlinear limit the $\beta$-Fermi-Pasta-Ulam ($\beta$-FPU) system in thermal equilibrium behaves surprisingly like weakly nonlinear waves in properly renormalized normal variables. This arises because the collective effect of strongly nonlinear interactions effectively renormalizes linear dispersion frequency and leads to effectively weak interaction among these renormalized waves. Furthermore, we show that the dynamical scenario for thermalized $\beta$-FPU chains is spatially highly localized discrete breathers riding chaotically on spatially extended, renormalized waves.

A universal sliding friction mechanism between soft, electrically charged surfaces (e.g., those carrying polyelectrolytes) is proposed. The Coulomb field of the randomly distributed charges induces a damped motion of the charges of the opposite surface, which gives rise to dissipation, and thus to friction. It is predicted that this friction force, which diverges at zero separation, may overcome viscous friction at distances significantly exceeding the Bjerrum length. This is not only of fundamental interest, but also of potential importance in life science and many practical situations.

We investigate chemical activity in hydrodynamical flows in closed containers. In contrast to open flows, in closed flows the chemical field does not show a well-defined fractal property; nevertheless, there is a transient filamentary structure present. We show that the effect of the filamentary patterns on the chemical activity can be modeled by the use of time-dependent effective dimensions. We derive a new chemical rate equation, which turns out to be coupled to the dynamics of the effective dimension, and predicts an exponential convergence. Previous results concerning activity in open flows are special cases of this new rate equation.

The spectral shape and observed sonoluminescence emission from Xe bubbles in concentrated sulfuric acid is consistent only with blackbody emission from a spherical surface that fills the bubble. The interior of the observed 7000 K blackbody must be at least 4 times hotter than the emitting surface in order that the equilibrium light-matter interaction length be smaller than the radius. Bright emission is correlated with long emission times ($\sim 10\mathrm{ns}$), sharp thresholds, unstable translational motion, and implosions that are sufficiently weak that contributions from the van der Waals hard core are small.

Optical vortices (nodal lines and phase singularities) are the generic singularities of scalar optics but are unstable in vector optics. We investigate experimentally and theoretically the unfolding of a uniformly polarized optical vortex beam on propagation through a birefringent crystal and characterize the output field in terms of polarization singularities (C lines and points of circular polarization; L surfaces and lines of linear polarization). The field is described both in the 2-dimensional transverse plane, and in three dimensions, where the third is abstract, representing an optical path length propagated through the crystal. Many phenomena of singular optics, such as topological charge conservation and singularity reconnections, occur naturally in the description.

We study the spreading of viscous drops on a solid substrate, taking into account the effects of thermal fluctuations in the fluid momentum. A nonlinear stochastic lubrication equation is derived and studied using numerical simulations and scaling analysis. We show that asymptotically spreading drops admit self-similar shapes, whose average radii can increase at rates much faster than these predicted by Tanner’s law. We discuss the physical realizability of our results for thin molecular and complex fluid films, and predict that such phenomenon can in principal be observed in various flow geometries.

We put forward properties of solitons supported by optical lattices featuring topological dislocations and show that solitons experience attractive and repulsive forces around the dislocations. Suitable arrangements of dislocations are even found to form soliton traps, and the properties of such solitons are shown to crucially depend on the trap topology. The uncovered phenomenon opens a new concept for soliton control and manipulation, e.g., in disk-shaped Bose-Einstein condensates.

High-order harmonic generation is demonstrated to provide a sensitive way for an extensive study of dynamic processes in the field-free alignment of strong-field-induced molecular rotational wave packets. The time-dependent harmonic signal observed from field-free-aligned ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{CO}}_2$ has been found to include two sets of beat frequency for pairs of coherently populated rotational states. One of them is the well-known frequency component characterizing the field-free alignment of molecules, and the other is ascribed to the beat that arises from coherence embedded in the wave packet. We discuss the effect of each frequency component on the revival signal observed with the harmonic generation.

We present a rigorous formalism of information transfer for systems with dynamics fully known. This follows from an accurate classification of the mechanisms for the entropy change of one component into a self-evolution plus a transfer from the other component. The formalism applies to both continuous flows and discrete maps. The resulting transfer measure possesses a property of asymmetry and is qualitatively consistent with the classical measures. It is further validated with the baker transformation and the Hénon map.

We present direct numerical simulations of two-dimensional decaying turbulence at initial Reynolds number $5\times {10}^4$ in a circular container with no-slip boundary conditions. Starting with random initial conditions the flow rapidly exhibits self-organization into coherent vortices. We study their formation and the role of the viscous boundary layer on the production and decay of integral quantities. The no-slip wall produces vortices which are injected into the bulk flow and tend to compensate the enstrophy dissipation. The self-organization of the flow is reflected by the transition of the initially Gaussian vorticity probability density function (PDF) towards a distribution with exponential tails. Because of the presence of coherent vortices the pressure PDF become strongly skewed with exponential tails for negative values.